Estimating the spatial scales of regionalized variables by nested sampling, hierarchical analysis of variance and residual maximum likelihood

The variogram is essential for local estimation and mapping of any variable by kriging. The variogram itself must usually be estimated from sample data. The sampling density is a compromise between precision and cost, but it must be sufficiently dense to encompass the principal spatial sources of variance. A nested, multi-stage, sampling with separating distances increasing in geometric progression from stage to stage will do that. The data may then be analyzed by a hierarchical analysis of variance to estimate the components of variance for every stage, and hence lag. By accumulating the components starting from the shortest lag one obtains a rough variogram for modest effort. For balanced designs the analysis of variance is optimal; for unbalanced ones, however, these estimators are not necessarily the best, and the analysis by residual maximum likelihood (REML) will usually be preferable. The paper summarizes the underlying theory and illustrates its application with data from three surveys, one in which the design had four stages and was balanced and two implemented with unbalanced designs to economize when there were more stages. A Fortran program is available for the analysis of variance, and code for the REML analysis is listed in the paper. (c) 2005 Elsevier Ltd. All rights reserved.

Hydraulic modeling of runoff over a rough surface under partial inundation

This study presents a numerical method to derive the Darcy- Weisbach friction coefficient for overland flow under partial inundation of surface roughness. To better account for the variable influence of roughness with varying levels of emergence, we model the flow over a network which evolves as the free surface rises. This network is constructed using a height numerical map, based on surface roughness data, and a discrete geometry skeletonization algorithm. By applying a hydraulic model to the flows through this network, local heads, velocities, and Froude and Reynolds numbers over the surface can be estimated. These quantities enable us to analyze the flow and ultimately to derive a bulk friction factor for flow over the entire surface which takes into account local variations in flow quantities. Results demonstrate that although the flow is laminar, head losses are chiefly inertial because of local flow disturbances. The results also emphasize that for conditions of partial inundation, flow resistance varies nonmonotonically but does generally increase with progressive roughness inundation.

Estimating the spatial scales of regionalized variables by nested sampling, hierarchical analysis of variance and residual maximum likelihood

The variogram is essential for local estimation and mapping of any variable by kriging. The variogram itself must usually be estimated from sample data. The sampling density is a compromise between precision and cost, but it must be sufficiently dense to encompass the principal spatial sources of variance. A nested, multi-stage, sampling with separating distances increasing in geometric progression from stage to stage will do that. The data may then be analyzed by a hierarchical analysis of variance to estimate the components of variance for every stage, and hence lag. By accumulating the components starting from the shortest lag one obtains a rough variogram for modest effort. For balanced designs the analysis of variance is optimal; for unbalanced ones, however, these estimators are not necessarily the best, and the analysis by residual maximum likelihood (REML) will usually be preferable. The paper summarizes the underlying theory and illustrates its application with data from three surveys, one in which the design had four stages and was balanced and two implemented with unbalanced designs to economize when there were more stages. A Fortran program is available for the analysis of variance, and code for the REML analysis is listed in the paper. (c) 2005 Elsevier Ltd. All rights reserved.

Scale-invariant moving finite elements for nonlinear partial differential equations in two dimensions

A scale-invariant moving finite element method is proposed for the adaptive solution of nonlinear partial differential equations. The mesh movement is based on a finite element discretisation of a scale-invariant conservation principle incorporating a monitor function, while the time discretisation of the resulting system of ordinary differential equations is carried out using a scale-invariant time-stepping which yields uniform local accuracy in time. The accuracy and reliability of the algorithm are successfully tested against exact self-similar solutions where available, and otherwise against a state-of-the-art h-refinement scheme for solutions of a two-dimensional porous medium equation problem with a moving boundary. The monitor functions used are the dependent variable and a monitor related to the surface area of the solution manifold. (c) 2005 IMACS. Published by Elsevier B.V. All rights reserved.

Are polyphagous geometrid moths with flightless females adapted to budburst phenology of local host species?

The majority of studies demonstrating local adaptation of insect herbivores involve sessile species, particularly those with a parthenogentic phase to their life history or endophagous "parasites" of plants. Current arguments suggest the strength of selection determines whether local adaptation can or cannot take place. Therefore local adaptation should not be limited to species with such traits. We studied the ability of three polyphagous geometrid moths with flightless adult females (Erannisdefoliaria, Operophtera brumata and O. fagata) to synchronise their egg hatching with the budburst of a local host species in north east Scotland. A strong selection for hatching time is expected among generalist moths given the large variation in budburst phenology and an inability to hatch in synchrony with budburst decreases moth fitness substantially. In two successive seasons, we trapped emerging females from patches of five host species and recorded the temperature sum needed for 50% egg hatch of each brood laid by the trapped females. The hatching times of broods were compared against the average budburst time of the maternal host species in the study area. In addition, the trapping dates of each female were recorded. Only O. brumata showed synchrony with egg hatch and budburst which suggests local phenological adaptation to different host species. This could be maintained by selection and partial reproductive isolation between populations dwelling on different host species. No phenological adaptation was found in the other common geometrids of the study area

The distributed work of local action: interaction amongst virtually collocated research teams

Existing research on synchronous remote working in CSCW has highlighted the troubles that can arise because actions at one site are (partially) unavailable to remote colleagues. Such ‘local action’ is routinely characterised as a nuisance, a distraction, subordinate and the like. This paper explores interconnections between ‘local action’ and ‘distributed work’ in the case of a research team virtually collocated through ‘MiMeG’. MiMeG is an e-Social Science tool that facilitates ‘distributed data sessions’ in which social scientists are able to remotely collaborate on the real-time analysis of video data. The data are visible and controllable in a shared workspace and participants are additionally connected via audio conferencing. The findings reveal that whilst the (partial) unavailability of local action is at times problematic, it is also used as a resource for coordinating work. The paper considers how local action is interactionally managed in distributed data sessions and concludes by outlining implications of the analysis for the design and study of technologies to support group-to-group collaboration.

Modeling electrocortical activity through improved local approximations of integral neural field equations

Neural field models of firing rate activity typically take the form of integral equations with space-dependent axonal delays. Under natural assumptions on the synaptic connectivity we show how one can derive an equivalent partial differential equation (PDE) model that properly treats the axonal delay terms of the integral formulation. Our analysis avoids the so-called long-wavelength approximation that has previously been used to formulate PDE models for neural activity in two spatial dimensions. Direct numerical simulations of this PDE model show instabilities of the homogeneous steady state that are in full agreement with a Turing instability analysis of the original integral model. We discuss the benefits of such a local model and its usefulness in modeling electrocortical activity. In particular, we are able to treat “patchy” connections, whereby a homogeneous and isotropic system is modulated in a spatially periodic fashion. In this case the emergence of a “lattice-directed” traveling wave predicted by a linear instability analysis is confirmed by the numerical simulation of an appropriate set of coupled PDEs.